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Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation.

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Presentation on theme: "Phase Transformation Chapter 9. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation."— Presentation transcript:

1 Phase Transformation Chapter 9

2 Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation An example of phase transformation

3 Czochralski crystal pulling technique How does one produce single crystal of Si for electronic applications?

4 Quenching of steel components a solid->solid phase transformation How does one harden a steel component?

5 Liquid solidification evaporation sublimation Solid gas melting condensation Solid state phase transformation Solid 21

6 Thermodynamic driving force for a phase transformation? Decrease in Gibbs free energy Liquid-> solid g s - g l = g = -ve

7 g gLgL gSgS g S < g L g L < g S Liquid is stable TmTm T Gibbs free energy as a function of temperature,Problem 2.3 gLgL gSgS g Solid is stable T freezing Fig. 9.1

8 How does solidification begins? Usually at the walls of the container Why? To be discussed later. Heterogeneous nucleation.

9 Spherical ball of solid of radius R in the middle of the liquid at a temperature below T m Homogeneous nucleation g L = free energy of liquid per unit volume g S = free energy of solid per unit volume r g = g S - g L

10 Change in free energy of the system due to formation of the solid ball of radius r : r +ve: barrier to nucleation r r*r* 2 4r

11 r r*r* 2 4r Solid balls of radius r < r* cannot grow as it will lead to increase in the free energy of the system !!! Solid balls of radii r > r* will grow r* is known as the CRITICAL RADIUS OF HOMOGENEOUS NUCLEATION

12 r r*r* 2 4r Eqn. 9.5 Eqn. 9.4

13 T g TmTm gLgL gSgS T g (T) Eqn. 9.7 Driving force for solidification

14 2 4r 2 4r f r Eqn. 9.8 Eqn. 9.7 Fig. 9.3 r1*r1* f 1 * f 2 * r2*r2* T1T1 T 2 <

15 Critical particle Fig. 9.4 Formation of critical nucleus by statistical fluctuation Atoms surrounding the critical particle Diffuse jump of a surrounding atom to the critical particle makes it a nucleation

16 The Nucleation Rate N t =total number of clusters of atoms per unit volume N* = number of clusters of critical size per unit volume By Maxwell-Boltzmann statistics

17 s*= no. of liquid phase atoms facing the critical sized particle H d = activation energy for diffusive jump from liquid to the solid phase = atomic vibration frequency The rate of successful addition of an atom to a critical sized paticle Eqn Eqn. 9.9

18 Rate of nucleation, I, (m 3 s -1 ) With decreasing T 1. Driving force increases 2. Atomic mobility decreases = No. of nucleation events per m 3 per sec = number of critical clusters per unit volume (N*) x rate of successful addition of an atom to the critical cluster ( ) Eqn T I TmTm

19 Growth Increase in the size of a product particle after it has nucleated T U

20 Overall Transformation Kinetics U I dX/dt T I :Nucleation rate U : Growth rate Overall transformation rate (fraction transformed per second) X=fraction of product phase

21 Fraction transformed as a function of time tsts tftf X t Slow due to very few nuclei Slow due to final impingement

22 TTT Diagram for liquid-to-solid transformation T Stable liquid Under Cooled liquid crystal Crystallization begins L+ Crystallization ends dX/dt T log t X tsts tftf 0 1 TmTm C- curves

23 L+ T Stable liquid Under Cooled liquid log t TmTm TTT Diagram for liquid-to-solid transformation U I T Coarse grained crystals Fine grained crystals glass

24 T log t t s metals t s SiO 2 H d log (viscosity) Metals: high h m, low viscosity SiO 2 : low h m, high viscosity Silica glass Metallic glass Eqn Eqn. 9.8

25 Cooling rate 10 6 ºC s -1 From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002) Melt Spinning for metallic glass ribbons

26 L+ T log t TmTm T TmTm TgTg Log (viscosity Pa-s) crystal Stable liquid Undercooled liquid glass 30 Fig. 9.17

27 TmTm Specific volume Stable liquid Undercooled liquid Fast cool Slow cool T gs T gf crystal Fig T

28 log t U I T L+ T Stable liquid Undercooled liquid TmTm devitrification time T Glass ceramics nucleation growth glass Glass ceramic Liquid glass crystal Very fine crystals TUTU TITI Fig. 9.16

29 Cornings new digital hot plates with Pyroceram TM tops. Corningware Pyroceram TM heat resistant cookware ROBAX® was heated until red- hot. Then cold water was poured on the glass ceramic from above - with NO breakage.

30 Czochralski crystal pulling technique for single crystal Si SSPL: Solid State Physics Laboratory, N. Delhi J. Czochralski, ( ) Polish Metallurgist

31 A Steel Hardness Rockwell C Wt% C Micro- structure Coarse pearlite fine pearlite bainite Tempered martensite martensite Heat treatment Annealing normalizing austempering tempering quenching B C D E TABLE 9.2

32 HEAT TREATMENT Heating a material to a high temperature, holding it at that temperature for certain length of time followed by cooling at a specified rate is called heat treatment

33 A N AT T Q heating holding time T AnnealingFurnace coolingRC 15 NormalizingAir coolingRC 30 QuenchingWater coolingRC 65 TemperingHeating after quenchRC 55 AustemperingQuench to an inter-RC 45 mediate temp and hold

34 Eutectoid Reaction cool Pearlite Ammount of Fe 3 C in Pearlite Red Tie Line below eutectoid temp

35 Phase diagrams do not have any information about time or rates of transformations. We need TTT diagram for austenite-> pearlite transformation

36 Stable austenite unstable austenite TTT diagram for eutectoid steel start finish

37 Stable austenite unstable austenite start finish Annealing: coarse pearlite Normalizing: fine pearlite U I T TTT diagram for eutectoid steel

38 Callister

39 Stable austenite unstable austenite start finish TTT diagram for eutectoid steel A+M M MsMs MfMf M s : Martensite start temperature M f : Martensite finish temperature : martensite (M) QUENCHING Hardness R C 65 Extremely rapid, no C-curves

40 BCT Amount of martensite formed does not depend upon time, only on temperature. Atoms move only a fraction of atomic distance during the transformation: 1. Diffusionless (no long-range diffusion) 2. Shear (one-to-one correspondence between and atoms) 3. No composition change Martensitic transformation

41 Problem 3.1 BCT unit cell of (austenite) BCT unit cell of (martensite) 0% C (BCC)1.2 % C Contract ~ 20% Expand ~ 12% Martensitic transformation (contd.) Fig. 9.12

42 Hardness of martensite as a function of C content Wt % Carbon Hardness, R C Hardness of martensite depends mainly on C content and not on other alloying additions Fig Martensitic transformation (contd.)

43 A N AT T Q heating T

44 Heating of quenched steel below the eutectoid temperature, holding for a specified time followed by ar cooling. TEMPERING T

45 Tempering (contd.) +Fe 3 CPEARLITE A distribution of fine particles of Fe 3 C in matrix known as TEMPERED MARTENSITE. Hardness more than fine pearlite, ductility more than martensite. Hardness and ductility controlled by tempering temperature and time. Higher T or t -> higher ductility, lower strength

46 Tempering Continued Callister

47 Austempering Bainite Short needles of Fe 3 C embedded in plates of ferrite

48 Problems in Quenching Quench Cracks High rate of cooling: surface cooler than interior Surface forms martensite before the interior AustenitemartensiteVolume expansion When interior transforms, the hard outer martensitic shell constrains this expansion leading to residual stresses

49 But how to shift the C-curve to higher times? Solution to Quench cracks Shift the C-curve to the right (higher times) More time at the nose Slower quenching (oil quench) can give martensite

50 By alloying All alloying elements in steel (Cr, Mn, Mo, Ni, Ti, W, V) etc shift the C-curves to the right. Exception: Co Substitutional diffusion of alloying elements is slower than the interstitial diffusion of C

51 Plain C steel Alloy steel Alloying shifts the C-curves to the right. Separate C-curves for pearlite and bainite Fig. 9.10

52 Hardenability Ability or ease of hardening a steel by formation of martensite using as slow quenching as possible Alloying elements in steels shift the C-curve to the right Alloy steels have higher hardenability than plain C steels.

53 HardnenabilityHardness Ability or ease of hardening a steel Resistance to plastic deformation as measured by indentation Only applicable to steelsApplicable to all materials Alloying additions increase the hardenability of steels but not the hardness. C increases both hardenability and hardness of steels.

54 High Speed steel Alloy steels used for cutting tools operated at high speeds Cutting at high speeds lead to excessive heating of cutting tools This is equivalent to unintended tempering of the tools leading to loss of hardness and cutting edge Alloying by W gives fine distribution of hard WC particles which counters this reduction in hardness: such steels are known as high speed steels.

55 Airbus A380 to be launched on October 2007

56 A shop inside Airbus A380

57 Alfred Wilms Laboratory Steels harden by quenching Why not harden Al alloys also by quenching?

58 time Wilms Plan for hardening Al- 4%Cu alloy Sorry! No increase in hardness. 550ºC T Heat Quench Hold Check hardness Eureka ! Hardness has Increased !! One of the greatest technological achievements of 20 th century

59 Hardness increases as a function of time: AGE HARDENING Property = f (microstructure) Wilm checked the microstructure of his age-hardened alloys. Result: NO CHANGE in the microstructure !!

60 As- quenched hardness Hardness time Peak hardness Overaging Hardness initially increases: age hardening Attains a peak value Decreases subsequently: Overaging

61 + : solid solution of Cu in FCC Al : intermetallic compound CuAl 2 4 T solvus supersaturated saturated + FCC Tetragonal 4 wt%Cu0.5 wt%Cu54 wt%Cu Precipitation of in

62 Stable unstable T solvus As- quench ed start finsh + Aging TTT diagram of precipitation of in A fine distribution of precipitates in matrix causes hardening Completion of precipitation corresponds to peak hardness

63 -grains As quenched -grains + AgedPeak aged Dense distribution of fine overaged Sparse distribution of coarse Driving force for coarsening / interfacial energy

64 hardness Aging time (days) 180ºC 100ºC 20ºC Aging temperature Peak hardness is less at higher aging temperature Peak hardness is obtained in shorter time at higher aging temperature Fig. 9.15

65 U I T Stable unstable As- quenched start finsh + Aging T solvus 1 hardness 180ºC 100ºC 20ºC 100 ºC 180 ºC

66 Recovery, Recrystallization and grain growth Following slides are courtsey Prof. S.K Gupta (SKG) Or Prof. Anandh Subramaniam (AS)

67 Cold work dislocation density point defect density Plastic deformation in the temperature range above(0.3 – 0.5) T m COLD WORK Point defects and dislocations have strain energy associated with them (1 -10) % of the energy expended in plastic deformation is stored in the form of strain energy AS

68 Cold work Hardness Strength Electrical resistance Ductility AS

69 Cold work Anneal Recrystallization Recovery Grain growth AS

70 Recovery, Recrystallization and Grain Growth During recovery 1. Point Defects come to Equilibrium 2. Dislocations of opposite sign lying on a slip plane annihilate each other (This does not lead to substantial decrease in the dislocation density) SKG

71 POLYGONIZATION Bent crystal Low angle grain boundaries Polygonization AS

72 Recrystallization Strained grains Strain-free grains Driving force for the Process = Stored strain energy of dislocations SKG

73 Recrystallization Temperature: Temperature at which the 50% of the cold-worked material recrystallizes in one hour Usually around 0.4 T m (m.p in K) SKG

74 Factors that affect the recrystallization temperature: 1. Degree of cold work 2. Initial Grain Size 3. Temperature of cold working 4. Purity or composition of metal Solute Drag Effect Pinning Action of Second Phase Particle SKG

75 Solute Drag Effect SKG

76 Grain Boundary Pinning SKG

77 Grain Growth Increase in average grain size following recrystallization Driving Force reduction in grain boundary energy Impurities retard the process SKG

78 Grain growth Globally Driven by reduction in grain boundary energy Locally Driven by bond maximization (coordination number maximization) AS

79 Bonded to 4 atoms Bonded to 3 atoms Direction of grain boundary migration Boundary moves towards its centre of curvature JUMP AS

80 Hot Work and Cold Work Hot Work Plastic deformation above T Recrystallization Cold Work Plastic deformation below T Recrystallization Cold Work Hot Work Recrystallization temperature (~ 0.4 T m ) AS

81 Cold work Recovery Recrystallization Grain growth Tensile strength Ductility Electical conductivity Internal stress Fig %CW Annealing Temperature AS

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